Atkin-Lehner |
2- 3+ 11+ |
Signs for the Atkin-Lehner involutions |
Class |
69696ea |
Isogeny class |
Conductor |
69696 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
135168 |
Modular degree for the optimal curve |
Δ |
-4074533610048 = -1 · 26 · 33 · 119 |
Discriminant |
Eigenvalues |
2- 3+ -4 0 11+ 4 -2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,3993,0] |
[a1,a2,a3,a4,a6] |
j |
1728 |
j-invariant |
L |
1.8659172492566 |
L(r)(E,1)/r! |
Ω |
0.46647931484118 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
4 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
69696ea1 34848a2 69696dy1 69696eb1 |
Quadratic twists by: -4 8 -3 -11 |